Y-12=1.5(x-4) get Y by it self

Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π

lorasvet [3.4K]

The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The instantaneous rate of change at a given value of $x$ can be found by concept of derivative, which is described below:

$g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Where $h$ is the difference rate.

In this question we must find an expression for the instantaneous rate of change of $g$ if $f(x) = \sin x$ and evaluate the resulting expression for $x = \frac{\pi}{3}$ . Then, we have the following procedure below:

$g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x$

$g(x) = \cos x$

Now we evaluate $g(x)$ for $x = \frac{\pi}{3}$ :

$g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}$

The instantaneous rate of change of g with respect to x at x = π/3 is 1/2. $\blacksquare$

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

4 0

2 years ago

To amend U.S. Constitution, 3/4 of the 50 states must approve the amendment. If 35 states approve an amendment, will the Constit

Elodia [21]

To answer the question we need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be ammended, and that is represented like this:
35/50 >= 3/4
that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify the fractions to compare easily:
35/50 >= 3/4
7/10 >= 3/4
now we need to find the least common multiplier of 10 and 4 to take the fractions to a common denominator and compare easy. Lets multiply numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:
7/10 >= 3/4
(2/2)(7/10) >= (5/5)(3/4)
2*7/2*10 >= 5*3/5*4
14/20 >= 15/20
we can see that the inequality does not hold, so,
35/50 >= 3/4
does not hold either, therefore the Constitution cannot be ammended

5 0

3 years ago

Read 2 more answers

76% of what number is 152?

Alexus [3.1K]

Answer:

200

Step-by-step explanation:

6 0

3 years ago

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Which statement is true about whether Z and B are

Dmitrij [34]

Answer:

Z and B are independent events because P(Z I B) = P(Z)

Step-by-step explanation:

If Z and B are independent, Z does not affect B and B does not affect Z.
This means that, to know something about B does not help predicting Z, and to know something about B does not help predicting Z.
Then, the probability P (Z/B) = P(Z) because B does not add any information about Z, therefore, the probability of Z only depends on itself.

6 0

3 years ago

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What is the value of a?

bekas [8.4K]

Answer:

A

Step-by-step explanation:

you do a/18=4/a, cross multiply

a^2=72

a=6 square root of 2

6 0

3 years ago